Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple question about bend light

  1. Feb 11, 2006 #1
    Does gravity bend light by pulling at the photons or does gravity curve the space-time the light travels through, making it appear that the light is bend?

    I thought it was the latter but I wasn't able to confirm it. I also run into a problem with black holes. A black hole must curve space-time back into itself to be a black hole if the latter is correct.

    Anyone? Thanks.
     
  2. jcsd
  3. Feb 11, 2006 #2

    Garth

    User Avatar
    Science Advisor
    Gold Member

    It is the latter. "gravity curves the space-time the light travels through"

    You can cobble together Newton and SR and treat photons as having a mass equivalent to their energy that is then attracted towards the Sun by a Newtonian gravitational force; but you only obtain half the observed value of angle of deflection, you haven't taken space curvature into account, which doubles that value to the full GR deflection.

    There is no problem with BHs, inside the event horizon the curvature tips the outgoing light cone over so that it does not reach out to the outside world.

    I hope this helps.

    Garth
     
  4. Feb 11, 2006 #3
    So in the case of a black hole space-time doesn't have to curve back into itself for it to be able to tip the light cone back into itself?

    If space-time around a black hole is tipped back into itself then that would seperate the space-time of the BH from the rest of the galaxy?

    Or am I applying everyday logic that has no validity?
     
  5. Feb 11, 2006 #4

    Garth

    User Avatar
    Science Advisor
    Gold Member

    You have to solve the equations of the Schwarzschild or Kerr metrics and work out where the null geodesics go. It is not easy to imagine without expert help, you might find Robert Wald's "Space Time and Gravity" helpful, or go the whole way and read his "General Relativity".

    Garth
     
  6. Feb 11, 2006 #5

    pervect

    User Avatar
    Staff Emeritus
    Science Advisor

    The Schwarzschild r-coordinate is a time coordinate inside the event horizon (though it's a space coordinate outside the horizon). Inside the event horizon of a black hole, time points towards the center (r=0).

    This can be thought of as "tipping light cones" as well, robphy has a diagram he likes to post that I'm too lazy to look up at the moment.

    Light can still reach the inside of a black hole from the outside, so the space-time in a black hole is not totally "separate" from that of the outside world.

    However, no event inside the black hole event horizon can affect anything outside the event horion, because no signal can propagate from the interior through the horizon.
     
  7. Feb 13, 2006 #6
    IMO, there's a lot easier way to intuit what's theorized than thinking of tipping light cones. The event horizon of a black hole is just where everything inflows at c. Search for “free-fall coordinates” here for a decent explanation.
     
  8. Dec 11, 2006 #7
    bending light in the lab.

    Probably discussed before?
    Wish to know if I can bend white light, or any visible light, in the lab, without using optics. IE, using strong magnets or electro-magnetic radiation/fields.
    PLEASE help!
     
  9. Dec 11, 2006 #8
    I think the problem you are having is that you are visualising in 3d still. The black hole doesn't need to bend space-time in on itself to bring something back to a position that it was previously at.

    Imagine that some light is trapped in a black hole, and that it is confined to a plane and orbiting in a circle for simplicity. If we plot what happens over time in 3d, using the plane that the light is orbiting in to reduce the 3d position down to 2d, then we can see a different view of the space time, and the light traces out a spiral path through it. There is no closed loop in time.
     
  10. Dec 11, 2006 #9
    I have looked at Einsteins original 1911 paper on the bending of light in which he used the fact that light is slowed down in a gravitational field and where he used Huygens principle to derive the deflected angle and which resulted in a deflection angle which was a factor two too low. It is easy to show that the factor 2 was missed because the speed of light (in a gravitational field) as seen by a distant observer was only based on gravitational time dilatation. If one takes into account both gravitational time dilatation and gravitational length contraction, the additional factor 2 comes out correctly (without having to solve the Einstein field equations).
     
  11. Dec 11, 2006 #10

    pervect

    User Avatar
    Staff Emeritus
    Science Advisor

    One usually solves for the motion of light (or for that matter test particles) by using the geodesic equations. This is not the only way to solve for the motion of light - as you mention, there is the possibility of using Huygen's principle (mathematically the Hamilton-Jacobi method). I haven't read the original Einstein paper of which you speak (if I have, I've forgotten it), but this is mentioned for instance by MTW on pg 1102.

    Neither of these approaches for finding the motions of particles involves solving Einstein's field equations if one already has the metric. Of course, the field equations are generally needed to find the metric in the first place. In this example the EFE were used to get the Schwarzschild metric.

    Another interesting point is that the fact that particles follow geodesics in the first place can be proved from the field equations in GR (rather than having to be assumed as a separate assumption). See for instance MTW pg 471. Given a region of space-time containing nothing but electromagnetic fields and the Maxwell stress-energy tensor, Maxwell's equations "pop out" of the Einstein field equations - they don't have to be separately assumed.

    This is drifting away from the main point. The main point is that there is a very close link between what you are calling "gravitational length dilation", and what Garth is calling "the curvature of space.
     
  12. Dec 11, 2006 #11
    Yes, you are right in that. I wonder whether one could derive the gravitational length contraction by using only the equivalence between acceleration and gravitational field. For time dilatation, simple arguments (both in special relativity and in general relativity) give the correct relations. Have you ever seen a "simple" derivation of gravitational length contraction (in the same "spirit" as for time dilatation) ?
     
  13. Dec 11, 2006 #12

    pervect

    User Avatar
    Staff Emeritus
    Science Advisor

    Consider the Rindler metric (in geometric units)

    (1+gz)^2 dt^2 - dx^2 - dy^2 - dz^2

    This metric is a vacuum solution to Einstein's field equations, and can be thought of as the (not necessarily unique) metric associated with an accelerated coordinate system.

    Because the coefficient of dx^2, dy^2 and dz^2 is unity, there is however no "gravitational length contraction" at all in this metric - if I understand your usage of the term correctly (it's possible I'm misunderstanding something here).

    So if I'm following your usage correctly, Schwarzschild coordinates have gravitational length contraction, but Rindler coordinates do not.

    The discussion is complicated by the fact that defining gravitational length contraction by looking at the metric coefficients is a coordinate dependent notion, so the same space-time can have gravitational length contraction in one set of coordinates, and not have it in another.
     
  14. Dec 11, 2006 #13
    Does this extra factor of two only apply to light and not massive objects, and if so, why?
     
  15. Dec 11, 2006 #14

    pervect

    User Avatar
    Staff Emeritus
    Science Advisor

    A particle moving at almost the speed of light will be deflected in almost the same manner as a particle moving at the speed of light - i.e. a neutrino, having a very small rest mass, moving at almost the speed of light, will follow essentially the same trajectory as a photon (which has zero rest mass).
     
  16. Dec 12, 2006 #15
    Hi, thanks, but this is not what I had in mind. I meant some simple derivation (without a pre-knowledge of the metric) using some simple set-up with light pulses bouncing of mirrors (as used for instance in some derivations for time dilatation). PS : I found the original paper (see below) of Einstein on Internet. I is of course in German (I have lived for 12 years in Germany, so for me that is no problem) but English translations should certainly exist.

    http://www.physik.uni-augsburg.de/annalen/history/papers/1911_35_898-908.pdf

    I wonder whether such a paper would be accepted today: it is not full of maths, it contains revolutionary ideas, it is not written in Latex and it contains some typographic errors and a reference without the year of publication ...:smile:
     
  17. Dec 12, 2006 #16
    Hi, I just found a very simple derivation of gravitational length contraction, without pre-knowledge of the metric. It is only based on the equivalence between acceleration and gravitation (rougly speaking). So, combining then gravitational time dilatation and gravitational length contraction, one can use this to the correct of speed of light in a gravitational field and the bending of light (around the sun for instance) can then be described by a simple refractive effect and it would give exactly the same result as the light bending obtained by general relativity. So, one could hold the alternative view that gravitation modifies the properties of the surrounding vacuum (such as electrical permittivity and magnetic permeability) such that the speed of light (and other things) is modified as a consequence of this. The mathematical equations would remain the same but the interpretation is very different. One replaces effectively "curvature of spacetime" by "modification of the quantum vacuum".
     
  18. Dec 12, 2006 #17
    Right, but doesn't the new interpretation derive from GR in the first place... in which case, why go to all of that bother when you already have a perfectly good theory with a simpler interpretation?

    I am not even sure if your idea is correct in the first place... AFAIK modifying electrical permittivity to create gravitational effects would require that other effects be observed.
     
    Last edited: Dec 12, 2006
  19. Dec 12, 2006 #18
    Yes, indeed, GR is a very good and precise theory but a stumbling block for a quantum gravity theory is precisely that GR is based on a purely geometrical description. By using a different interpretation (in terms of the quantum vacuum) one could come a step closer in realizing this goal.
     
  20. Dec 12, 2006 #19
    I think that it is naive to assume that curvature is a stumbling block for quantum gravity and that it must be based on a background flat space-time.

    If we don't make that assumption it doesn't hurt us, since flat is just a special case of curved we could "come out with" a flat space-time for a QG theory anyway.

    There is a paper floating around somewhere that demonstrates that even if you do start from a flat space time with the weak field approximation, the flat space-time becomes physically unobservable and a curved space-time is 'induced' by the presense of a gravitational field... I will see if I can find it.

    That and I'm sure that I have read in numerous places that the real issue is renormalisation, since all of the 'charges' (masses) are positive there are no known ways to remove the infinities from the renormalisation.

    Renormalisation is something that should be done away with more than curvature in my opinion... it is a rather arbitrary process, the sort of thing I would do (have done) in a computer program to force something to give results in an expected range. The only valid use I see is to normalise *one* thing, e.g. a vector, to get a unit vector. Renormalising a whole field just seems wrong from my narrow perspective... in my opinion a better solution (probably not possible though) would be a wave equation which produces already normalised values. Sure, nothing would ever add up to 100%, but you would have the right answers and would have done away with an ugly feature.
     
  21. Dec 12, 2006 #20

    pervect

    User Avatar
    Staff Emeritus
    Science Advisor

    The super-simple (perhaps over-simplified) version of what I've been trying to say is that while gravitation is always associated with time dilation, it may or may not be associated with length contraction. For instance, there is no length contraction due to gravity in the elevator gerdankenexperiment, (though there is time dilation).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Simple question about bend light
Loading...